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MODULE CODE PH-104

TITLE OF MODULE INTRODUCTION TO ASTRONOMY AND COSMOLOGY

CREDIT POINTS 10

LEVEL 1

SEMESTER 1

CONTACT HOURS 28

PRE-REQUISITE

CO-REQUISITE

LECTURER/S Prof D C Dunbar

MONITOR/S Dr C R Allton

METHOD OF ASSESSMENT

20% Continuous Assessment and 80% Written Examination

OBJECTIVES To provide a broad view of Modern Astronomy.

SYLLABUS 1. Earth Based Observations 2. Schemes of the Solar System 3. A Modern view of the solar system 4. Exploration of the Solar System 5. Planetary Zoology 6. Understanding our Sun 7. Understanding Stars 8. The Birth of Stars 9. Stellar Death 10. Red Giants, Supernovae, Neutron Stars and Black Holes 11. Galaxies 12. The Universe: stars galaxies, distances times and masses 13. The Expanding Universe and its Thermal History 14. The Contents of the Universe

LEARNING OUTCOMES

1. An understanding of modern astronomy

SUGGESTED READING 1. “Universe” 7th Edition by R Freedman & W Kaufmann ISBN 0-7167-8694-X.

2. “Discovering the Universe” 6th Edition by N Comins and W Kaufmann ISBN 0-7167-9673-2.

3. “The First Three Minutes” by S Weinberg ISBN 0-465-024378

DEPARTMENT OF PHYSICS MODULE DATA

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MAG130 Mathematics for Scientists 1*Semester 1 Assessment by Coursework 20%Lecturer Dr AD Thomas Assessment by Examination 80%10 UWS credits, 5 ECTS credits Exam January, length 2 hours

The continuous assessment component comprises 4 exercise sheets, each worth 5%.At the end of this module, the student should:• know how to calculate with complex numbers• understand the meaning of continuity and differentiability• have learned the methods for differentiation for functions of a single variable• have learned the methods for integration for functions of a single variable

Syllabus:Basics of algebraic manipulation and use of brackets.Functions of a real variable, sketching graphs and asymptotes. Even and odd functions, 1-1 functions and their inverses. The inverse trig functions. Powers, exponentials and logs (base e, 2 and 10). The binomial expansion for integer powers and the binomial coefficients.Quadratic equations, roots and complex numbers. Complex arithmetic, including conjugate, modulus and argument. De Moivre's theorem and nth roots.Continuous and discontinuous functions, left and right limits (to be done by looking at graphs). The slope of a graph. Derivatives, including trig, exp and log functions. The rules for differentiating a sum, product and quotient. The chain rule and derivatives of inverse functions. Applications of calculus to find maxima, minima and curve sketching. Points of inflection.Areas under graphs, integration as a reverse to differentiation. Definite integrals, indefinite integrals. Some standard integrals. Methods of integration: substitution, parts and partial fractions.

Recommended Reading: Needed by

Dennis T Christy, Pre calculus, W.C. Brown, 1993, QA331.3.CHR2, [Primary] MAG131MAG133

DW Jordan & P Smith, Mathematical Techniques, OUP, 1994, TA303.JOR, [Primary]

SG Krantz, Calculus Demystified, McGraw Hill, 2003, [Primary]

F Safier, Schaum's Outline of Precalculus, McGraw Hill, 1998, [Primary]

* Cannot be taken as part of a Mathematics Degree Scheme.

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MAG131 Mathematics for Scientists 2*Semester 2 Assessment by Coursework 30%Lecturer Dr EJ Beggs Assessment by Examination 70%10 UWS credits, 5 ECTS credits Exam June, length 2 hours

The continuous assessment component is 15% from exercise sheets, and 15% from computing exercises.At the end of this module, the student should: Pre/Coreq• be able to set up a simple mathematical model of a real world situation MAG130 C• know analytical techniques for solving first and second order ODEs• be able to solve (using computers if necessary) the ordinary differential equations resulting from simple models• understand interdependence of Calculus and the theory of ODEs• be able to analyse models of growth and decay and state the corresponding initial value problems for ODEs

Syllabus:Mathematical modelling: How to set up differential equations.First order differential equations.Separation of variables.Population growth, the logistic equation, radioactive decay.Integrating factor method.Second order equations with constant coefficients.Homogeneous and non-homogeneous equations.Damping and resonance.Complementary functions and particular integrals.Taylor series, and series solutions of differential equations.Special cases of series solutions.Nonlinear differential equations and equations with several dependent variables, e.g. the predator-prey equations or enzymemediated chemical reactions.

Computing (Mathematica) Starting Mathematica. Basic arithmetic and the use of brackets. Plotting graphs of functions of one variable. The Solve and NSolve commands. Complex numbers. Differentiation and integration. Numerical integration. Solving ordinary differential equations.

Recommended Reading: Needed by

DW Jordan & P Smith, Mathematical Techniques, OUP, 1994, TA303.JOR, [Secondary] MAG133

Stephen Wolfram, The Mathematica Book, 4th edn, CUP, 1999, QA76.95.WOL4, [Background]

* Cannot be taken as part of a Mathematics Degree Scheme.

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MAG133 Additional Maths for Scientists*Semester 2 Assessment by Coursework NoneLecturer Dr EJ Beggs Assessment by Examination 100%10 UWS credits, 5 ECTS credits Exam June, length 2 hours

At the end of this module, the student should: Pre/Coreq• know the methods for differentiation and integration for functions of several variables MAG130 C• understand the relevance of vectors and vector products to forces, work and turning moments MAG131 C• understand vector calculus which is vital for electrodynamics and fluid dynamics• be able to use vectors for solving problems with positions, velocities and geometry• be able to use Taylor series, including their use for solving differential equations

Syllabus:The Sinh and Cosh functions. Some trig identities. Functions of two and three variables. Partial derivatives and the chain rule for partial derivatives. Exact differentials and their physical significance (2 dimensions only). The gradient, divergence and curl of a vector field. Polynomials: Roots, factors and the remainder theorem. Finding approximate roots from graphs. Matrices and matrix arithmetic, determinants and inverses. Solving systems of linear equations. Matrices acting on vectors, eigenvectors and eigenvalues. Fourier series. Partial differential equations and separation of variables.The heat and wave equations.

Computing (Mathematica) Vectors. Plotting functions of two variables and partial derivatives. Polynomials and roots, the Factor command.

Recommended Reading:DW Jordan & P Smith, Mathematical Techniques, OUP, 1994, TA303.JOR, [Secondary]

Stephen Wolfram, The Mathematica Book, 4th edn, CUP, 1999, QA76.95.WOL4, [Background]* Cannot be taken as part of a Mathematics Degree Scheme

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